Stability of Critical Equilibrium States (Nonlinear Science)

This monograph deals with the stability of stationary solutions (equilibrium states) in ordinary differential equations. It examines the cases in which a linear approximation is insufficient to determine whether the equilibrium state is stable or not. The first chapters of the book are intended to be helpful to researchers of various specialities, using ordinary differential equations, and the rest are intended for use by mathematicians and specialists in mechanics interested in the general theory of stability of motion and the problems of nonlinear analysis. The authors consider the "frequency of occurrence" of the cases considered and all the cases included have a degeneracy level not greater than three. No preliminary knowledge on the subject of the book is required.